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Conditions of a Perfect Heat Engine.

609

mechanism; and, finally, reject a smaller quantity of heat into
some cold body. In the steam engine these ' bodies3 are the boiler
and condenser respectively. We shall see that the efficiency of
the engine does not depend on the working substance, if a rever-
sible cycle be adopted, but only on the difference of temperatures
between which the substance is utilised. A perfect heat engine
should have the following qualifications :

1.   The heat must be received at the temperature of the

hot body.

2.   The healt must be rejected at the temperature of the

cold body.

3.   The cycle must be reversible.

For perfect working, it is clear that all heat represented by
drop of temperature between the hot and cold bodies should
be delivered to the engine as work. But if there be a fall of
temperature between hot body and engine, or between engine
and cold body, some heat will be lost on the way which does
not reach the engine. Hence the reason for (i) and (2). We
may explain (3) similarly, first premising that by direct action we
mean the transformation of heat into work by abstraction of heat
from hot body; reversed action being obtained by turning the
engine backward, giving all the work'back to .the hot body. In
a perfect engine, the work given by the gas during one direct
cycle must equal the heat returned during one reversed cycle,
which is to say, that all the (available' heat must be transformed
into work.

Carnot's cycle fulfils these three conditions, and none other
can have a higher efficiency, as we shall prove. Fig. 617 is the
ideal engine, having a non-conducting cylinder A, and piston B,
the latter connected to suitable working mechanism, c is the
hot body, E the cold body, and D a non-conducting cylinder-
cover; and the underlying diagram indicates the changes we
are now to follow, First operation: Commencing with a portion
of gas behind the piston, at temperature ^ (that of the hot body),
pressure Px, and volume Vp we allow this to expand at constant
temperature while doing work Placing the left ,end of the
cylinder on the hot body, the expansion curve is the isothermal